Writing Linear Equations from Graph

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive slope goes up, negative slope goes down).

Front

What is the y-intercept (b) in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients in a linear equation determine the slope and the y-intercept, which define the line's steepness and where it crosses the y-axis.

Front

What does it mean if the slope of a linear equation is zero?

Back

If the slope is zero, the line is horizontal, indicating that y does not change as x changes.

Front

What does it mean if the slope of a linear equation is undefined?

Back

If the slope is undefined, the line is vertical, indicating that x does not change as y changes.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find the y-intercept, plot it on the graph, and use the slope to find another point.